2025/10/12 by J. Kawasaki, Kawasaki, Jun
Computer Science · Decision Sciences · #Advanced Database Systems and Queries #Data Quality and Management #Databases (cs.DB) #FOS: Computer and information sciences #Semantic Web and Ontologies
paper · pdf · doi:10.48550/arxiv.2512.02021
openalex publication_date 2025/10/12 · openalex created_date 2025/12/04 · openalex updated_date 2026/07/28
Conventional database architectures often secure local consistency by discarding information, entangling correctness with loss. We introduce the Functorial-Categorical Database (FCDb), which models data operations as morphisms in a layered functor category and establishes a Complete Preserving Family (CPF) of projections spanning content invariance (CAS), capability, and ownership, with optional observational projections for local order (B+Tree), temporal history (append-only/LSM), and adjacency (Graph). We identify a minimal kernel (Fcore = Own o Cap o CAS) that preserves information and collapses non-commutativity to the ethical grant/revoke boundary. Under adjoint lifts and a fibred structure, operational pairs commute in the categorical limit while ownership integrity and capability constraints are maintained. The framework connects to information geometry via projection interpretations and supports empirical validation without discarding semantic, temporal, or relational entropy.